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timholy merged 2 commits into from
Mar 8, 2026
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Ensure initializer produce feasible solutions #7

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Ensure initializer produce feasible solutions
timholy Mar 8, 2026
675cf7d
fix docs
timholy Mar 8, 2026
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6 changes: 3 additions & 3 deletions docs/src/index.md
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Expand Up @@ -79,15 +79,15 @@ julia> using ScaleInvariantAnalysis, JuMP, HiGHS
julia> A = [1 2 3; 6 5 4];

julia> a, b = cover(A)
([1.2544610775677627, 3.4759059767492304], [1.7261686708831454, 1.6581941714076147, 2.391465190627206])
([1.2674308473260654, 3.4759059767492304], [1.7261686708831454, 1.61137045961268, 2.366993044495631])

julia> aq, bq = cover_qmin(A)
([1.1986299970143055, 3.25358233351279], [1.8441211516912772, 1.6685716234216104, 2.5028574351324164])

julia> a * b'
2×3 Matrix{Float64}:
2.16541 2.08014 3.0
6.0 5.76373 8.31251
2.1878 2.0423 3.0
6.0 5.60097 8.22745

julia> aq * bq'
2×3 Matrix{Float64}:
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30 changes: 26 additions & 4 deletions src/covers.jl
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Expand Up @@ -81,7 +81,7 @@ function symcover(A::AbstractMatrix; kwargs...)
else
aprod = ai * aj
aprod >= Aij && continue
s = sqrt(Aij / sqrt(aprod))
s = sqrt(Aij / aprod)
a[i] = s * ai
a[j] = s * aj
end
Expand All @@ -108,12 +108,12 @@ See also: [`cover_lmin`](@ref), [`cover_qmin`](@ref), [`symcover`](@ref).
julia> A = [1 2 3; 6 5 4];

julia> a, b = cover(A)
([1.2544610775677627, 3.4759059767492304], [1.7261686708831454, 1.6581941714076147, 2.391465190627206])
([1.2674308473260654, 3.4759059767492304], [1.7261686708831454, 1.61137045961268, 2.366993044495631])

julia> a * b'
2×3 Matrix{Float64}:
2.16541 2.08014 3.0
6.0 5.76373 8.31251
2.1878 2.0423 3.0
6.0 5.60097 8.22745
```
"""
function cover(A::AbstractMatrix; kwargs...)
Expand Down Expand Up @@ -146,6 +146,28 @@ function cover(A::AbstractMatrix; kwargs...)
for j in axes(A, 2)
b[j] = iszero(nzb[j]) ? zero(T) : exp(logb[j] / nzb[j] - halfmu)
end
# Now we have sums of (log(a[i]) + log(b[j]) - log(A[i, j])) to be zero across rows or columns.
# Now it needs to be boosted to cover A.
for j in axes(A, 2)
for i in axes(A, 1)
Aij, ai, bj = abs(A[i, j]), a[i], b[j]
if iszero(bj)
if !iszero(ai)
b[j] = Aij / ai
else
a[i] = b[j] = sqrt(Aij)
end
elseif iszero(ai)
a[i] = Aij / bj
else
aprod = ai * bj
aprod >= Aij && continue
s = sqrt(Aij / aprod)
a[i] = s * ai
b[j] = s * bj
end
end
end
return tighten_cover!(a, b, A; kwargs...)
end

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13 changes: 11 additions & 2 deletions test/runtests.jl
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Expand Up @@ -134,16 +134,25 @@ using Test
sym_ratios = Float64[]
for (_, A) in symmetric_matrices
Af = Float64.(A)
a0 = symcover(Af; iter=0)
@test all(a0[i] * a0[j] >= abs(Af[i, j]) - 1e-12 for i in axes(Af, 1), j in axes(Af, 2))
a0 = symcover(Af / 100; iter=0)
@test all(a0[i] * a0[j] >= abs(Af[i, j])/100 - 1e-12 for i in axes(Af, 1), j in axes(Af, 2))
a = symcover(Af; iter=10)
lopt = cover_lobjective(symcover_lmin(Af), Af)
lfast = cover_lobjective(symcover(Af; iter=10), Af)
lfast = cover_lobjective(a, Af)
iszero(lopt) || push!(sym_ratios, lfast / lopt)
end
@test median(sym_ratios) < 1.01
@test median(sym_ratios) < 1.1

# cover cover_lobjective should be close to optimal (cover_lmin)
gen_ratios = Float64[]
for (_, A) in general_matrices
Af = Float64.(A)
a0, b0 = cover(Af; iter=0)
@test all(a0[i] * b0[j] >= abs(Af[i, j]) - 1e-12 for i in axes(Af, 1), j in axes(Af, 2))
a0, b0 = cover(Af / 100; iter=0)
@test all(a0[i] * b0[j] >= abs(Af[i, j])/100 - 1e-12 for i in axes(Af, 1), j in axes(Af, 2))
al, bl = cover_lmin(Af)
a, b = cover(Af; iter=10)
lopt = cover_lobjective(al, bl, Af)
Expand Down
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